This is not currently supported by HTML5 audio. However, new features are in the works which would allow for this kind of audio processing. I think modern javascript engines might actually be fast enough too, considering its pretty much all compiled to machine code now.

The new audio APIs are probably about six months away, and then there's no guarantee all browsers will support them (Internet Explorer is particularly slow and reluctant to adopt new standards). So you'll probably just have to wait it out for now I'm afraid.

How will they work -- will they be predefined effects whose parameters can be controlled in Construct2, or will we be able to design effects from the ground up (with something like Pure Data or Supercollider) and incorporate them in to Construct 2 (and then control the parameters in real-time.

Well, here's the Web Audio API which is a work in progress. It's seriously technical, but you can probably spot a few features, like DynamicsCompressor and BiquadFilter - other more complicated effects will probably have to be done in a JavaScriptAudio node, which means writing javascript to process the effect.

That's great news, and hopefully the browsers get up to speed with audio support quickly. I realize Construct is designed for game development but that type of audio processing would enable creation of Apps like Audiotool.com using it.